Multiple and Logistic Regression

Question 1

what is the equation for simple linear regression?

Answer 1

Y = mx+ c

OR

Y = B0 + B1X + E

Question 2

what is the equation for multiple linear regression?

Answer 2

Y = B0 + B1X + B2X + E

Y is dependent variable
X is the independent variable
B0 is the intercept
B1 is the slope of X1
B2 is the slope of X2
E is the error term

Question 3

give three times when can we use multiple linear regression?

Answer 3

• when we want to predict a continuous outcome variable (statistics exam score) from multiple predictor variables e.g. (IQ, watched lectures, hours of sleep)
• when independent variables are causally related to dependent to variable
• for hypothesis testing
• to predict how much the independent predictors explain the variation in the dependant predictors

Question 4

what is R^2?

Answer 4

the variability in the outcome variables that is predicted by the independent predictors

an r^2 value of 100% means all of the variation in the Y variable is caused by the independent predictors

Question 5

what are the 6 advantages of multiple linear regression

Answer 5

• able to adjust for confounding variables
• examine the effect of multiple independent predictors on an outcome
• improves amount of variability you can explain in the dependent variable
• perform multiple hypothesis tests
• more accurate predictions of outcome variable

Question 6

what is logistic regression used for?

Answer 6

used to predict a binary outcome variable (a “0” or a “1”)

Question 7

what 2 tyeps of predictors can we use for logistic regression?

Answer 7

• binary
• continuous

Question 8

what does the output need to be in logistic regression and why?

Answer 8

• needs to be between 0 and 1
• this is because we model probabilities as the outcome

Question 9

why can’t you use linear regression to predict passing an exam from hours of sleep?

Answer 9

linear regression output is negative to postivie infinity, but the relationship between probability and independent variables is not linear

Question 10

what is the inverse logisitic function equation?

Answer 10

e (B0 + B1x)
/
1 + e(B0 + B1x)

Question 11

what are log-odds/logits?

Answer 11

makes an inverse logit function show a linear relationship

Question 12

what is the equation for log odds

Answer 12

log(P/(1-P)) = B0 + B1X